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Lecture 09: Data Structure Transformations. Geography 128 Analytical and Computer Cartography Spring 2007 Department of Geography University of California, Santa Barbara.

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Lecture 09 data structure transformations

Lecture 09: Data Structure Transformations

Geography 128

Analytical and Computer Cartography

Spring 2007

Department of Geography

University of California, Santa Barbara


Why transform between structures

"In virtually all mapping applications it becomes necessary to convert from one cartographic data structure to another. The ability to perform these object-to-object transformations often is the single most critical determinant of a mapping system's flexibility" (Clarke, 1995)

Geocoding stamps coordinate system, resolution and projection onto objects

Data usually in generic formats at first

Can save space, gain flexibility, decrease processing time

Suit demands of analysis and modeling

Suit demands of map symbolization (e.g. fonts)

Why Transform Between Structures?


Generalization transformations why generalize

Conversion of data collected at higher resolutions to lower resolution. Less data and less detail.

Simplicity -> clarity

Information will be lost

Generalization Transformations- Why Generalize?

John Krygier and Denis Wood, Making Maps:

a visual guide to map design for GIS


Generalization transformations point to point

Centroid resolution. Less data and less detail.

Map projections

Usually be seen as a part of Geocoding process

Generalization Transformations - Point-to-Point

USGS 1:250,000 3-arc second DEM format (1-degree block)


Generalization transformations line to line generalization

N-th Point retention resolution. Less data and less detail.

Equidistant re-sampling

Douglas-Peucker

Generalization Transformations - Line-to-Line Generalization

Douglas-Peucker line generalization


Generalization transformations line to line enhancement

Splines resolution. Less data and less detail.

Bezier Curves

Polynomial Functions

Trigonometric Functions (Fourier-based)

Generalization Transformations - Line-to-Line Enhancement


Generalization transformations area to area

Problem is given one set of regions, convert to another resolution. Less data and less detail.

Example: Convert census tract data to zip codes for marketing

Example: Convert crime data by police precinct to school district

May require dividing non-divisible measures, e.g population

Areal Interpolation

Greatest common geographic units: Full overlap set for reassignment

Generalization Transformations - Area-to-Area

Population at counties

Population at watersheds=?


Generalization transformations area to area1

Algorithm for Overlay resolution. Less data and less detail.

1. Intersections

2. Chain splitting

3. Polygon reassembly

4. Labeling and attribution

Generalization Transformations - Area-to-Area


Generalization transformations volume to volume

Common conversion between two major data structures, vector (TIN) and grid

Often via points and interpolation

Change cell size

Generate a new grid

Compute the intersect

Interpolate from neighboring cells

Problem of VIPs

Generalization Transformations Volume-to-Volume

www.soi.city.ac.uk/~jwo/phd/04param.php


Vector to raster transformations

Easy compared to inverse, a form of re-sampling (TIN) and grid

Grid must relate to coordinates (extent, bounds, resolution, orientation)

Rasters can be square, rectangular, hexagonal.

Resample at minimum r/2

Vector-to-Raster Transformations

  • Problem: What value goes into the cell?

    • Dominant criterion

    • Center-point criterion

  • Separate arrays for dimensions and binary data?

  • Index entries & look up tables


Vector to raster transformations cnt algorithm

Convert form of vectors (e.g. to slope intercept) (TIN) and grid

Sample and convert to grid indices

Thin fat lines

Compute implicit inclusion (anti-alias)

Vector-to-Raster Transformations (cnt.)- Algorithm

www.inf.u-szeged.hu/~palagyi/skel/skel.html



Raster to vector transformations

Much harder, more error prone. (TIN) and grid

May involve cartographer intervention

Importance of alignment

Can do points, lines, area

Raster-to-Vector Transformations


Raster to vector transformations algorithm

Skeletonization and Thinning (TIN) and grid

Peeling

Expanding

Medial Axis

Feature Extraction

Topological Reconstruction

Raster-to-Vector Transformations- Algorithm


Raster to vector transformations edge detection

Grid Scan (TIN) and grid

Matrix Algebra - filtering

Raster-to-Vector Transformations- Edge Detection

fourier.eng.hmc.edu/.../gradient/node9.html


Data structure transformations

Scale transformations are lossy (TIN) and grid

(re)storage produce error

algorithmic error, systematic and random

Types are: scale, structural (data structure), dimensional, vector-to-raster

Data Structure Transformations


The role of error

Kate Beard: Source error, use error, process error (TIN) and grid

Morrison: Method-produced error

Error is inherent, can it be predicted, controlled or minimized?

XT = X'

X' T^-1 = X + E

The Role of Error

  • Errors are

    • positional

    • attribute

    • systematic

    • random

    • known

    • uncertain

    • Errors can be attributed to poor choice of transformations

    • Incompatible sequences of T's (non-invertible)

    • "Hidden" Error=use error, not process error


Next lecture

Map Design (TIN) and grid

Next Lecture


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